Question

Как найти неизвестную сторону в треугольнике при этом зная две стороны

Answer 1

Если есть периметр, то надо от него отнять сумму двух известных сторон

Answer 2

Finding the Unknown Side in a Triangle

To find the unknown side in a triangle when two sides are known, you can use the Law of Cosines. The Law of Cosines states that for any triangle with sides of length a, b, and c, and angles opposite those sides labeled A, B, and C, the following equation holds true:

c^2 = a^2 + b^2 - 2ab * cos(C)

Where: - c is the length of the side opposite angle C - a and b are the lengths of the other two sides - C is the measure of the angle opposite side c

By rearranging this equation, you can solve for the unknown side length. Let's denote the unknown side as x, and the known sides as a and b. The angle opposite the unknown side can be found using the fact that the sum of the angles in a triangle is 180 degrees.

x = sqrt(a^2 + b^2 - 2ab * cos(C))

This formula allows you to find the length of the unknown side when the lengths of the other two sides and the measure of the included angle are known.

Example Calculation

For example, if side a = 8 units, side b = 10 units, and the included angle C = 45 degrees, you can calculate the length of the unknown side using the formula:

x = sqrt(8^2 + 10^2 - 2*8*10 * cos(45))

x = sqrt(64 + 100 - 160 * 0.7071)

x = sqrt(164 - 113.1376)

x = sqrt(50.8624)

x ≈ 7.13 units

So, the length of the unknown side is approximately 7.13 units.

This method allows you to find the length of an unknown side in a triangle when the lengths of the other two sides and the included angle are known.

I hope this helps! If you have any other questions, feel free to ask.